How do I create the texture of the clouds in Illustrator?
Or is there a set of brushes that could give a similar effect someone can point me to?
(Images from samkalda.com)
There's no flood of answers because there's no perfect way to make those clouds in Illustrator. Grainy textures are much easier in Photoshop.
One possibility is to create a cloud in Photoshop and import a raster image to Illustrator. Or to create bigger piece of it and define the shapes and sizes in Illustrator with clipping masks. The result can well be acceptable if the resolution of the pasted raster image is good for your intended purpose. You lose the lossless scalability of vector images, but you can get a job done.
In Illustrator grainy textures are often made by painting with a brush which scatters small objects in a little randomized way and by inserting an opacity mask, if needed. Here's an example: https://www.youtube.com/watch?v=xwNInJssbPU
A low spec computer can harmfully slow down this way because the brush can very quickly generate for ex. ten thousand objects.
Some other vector drawing programs, for ex. Affinity Designer have avoided this by allowing noisy colors, the grain is a part of the color, it's processed in the graphics card engine, not in the application program. In your case one could use noisy gradients. Unfortunately Illustrator hasn't noisy colors which could be used in gradients.
If you can sacrifice the lossless scalability, you can make raster image patterns also in Illustrator, there's no need to create them in Photoshop. Here's one method:
A shape is drawn, no stroke, solid grey fill
A copy of the shape 1 has got a raster effect Texture > Grain > Stippled, intensity=100%, contrast=50%
NOTE: you must define the raster effect rendering resolution in the beginning when you start a new image. It can be changed afterwards for ex. by copying and pasting everything to a new Illustrator document which has different raster image rendering resolution. I selected 150 DPI which provided good grain size just in this case.
Another copy of the shape 1 have got vertical gradient fill. The color is white, but it's fully opaque in the bottom and fully transparent on the top.
Shape 2 is placed on a copy of shape 3, aligned and defined to be the opacity mask
Shape 3 is placed on the result of 4
Quite complex and not exactly a copy of your cloud, I say, but it is made in Illustrator.